Bring the vegetable broth to a boil in a medium saucepan. Add the frozen peas and cook until bright green and tender, about 3-5 minutes.
Transfer the peas and broth to a blender. Add the heavy cream, mint leaves, and lemon juice. Blend until smooth and creamy.
Season with salt and pepper to taste. Chill for at least 30 minutes.
While the soup chills, heat the olive oil in a small skillet over medium heat. Add the prosciutto and cook until crispy, about 3-5 minutes. Transfer to a paper towel-lined plate to drain.
Serve the chilled soup garnished with crispy prosciutto and fresh mint leaves.